The first couple traded the Beltway for the ‘burbs and bunked up in their Westchester home for the first time last night — with dreams of a Senate race dancing in their heads.

The president, Mrs. Clinton, and Mrs. Clinton’s mother, Dorothy Rodham, touched down at Westchester County Airport shortly after 6 p.m. and were immediately whisked via Secret Service caravan to their tony home in Chappaqua, 38 miles north of Midtown.

The 101-year-old, three-story house will serve as home base for Mrs. Clinton as she tries to succeed Daniel Patrick Moynihan in the U.S. Senate. In her way is Mayor Giuliani, the likely Republican candidate.

“I think every American can understand it’s quite an exciting event to move into a house,” White House spokesman Joe Lockhart said.

Mrs. Clinton and her mother were supposed to spend the night together in the 11-room Dutch colonial home. But Lockhart said an unexpected break in the president’s schedule allowed him to join them.

Without elaborating, Lockhart said a family friend who lives nearby brought dinner to the first family. The Clintons are scheduled to tell reporters this morning how their first night went in their first private home since 1982.

Lockhart said the Clintons were going to unpack some of their belongings, which arrived Tuesday, and then call it a night.

For most of the day, reporters and cameramen created a zoo-like atmosphere near Old House Lane — the cul-de-sac along which the Clintons will live. The town has barred parking on the small street for security reasons.

The house features four bathrooms, five bedrooms, a gym and a wraparound balcony that overlooks an outdoor pool.

At a City Hall press conference, the mayor snapped at a reporter who asked him about Westchester’s two newest residents.

But Giuliani later said: “I feel very, very proud of the fact that people from all around the country want to come to New York, including people from Arkansas.”

In his annual State of the State address, Gov. Pataki echoed the mayor’s comments, saying: “Why, even people from Hope, Arkansas, understand that New York is the best state to live.”

The Clintons bought their $1.7 million home on Nov. 1 by taking out a $1.36 million, 30-year loan.

The original financing package for the house sparked controversy after the White House revealed that Terry McAuliffe — a major Democratic donor — was putting up $1.35 million of his own money as collateral for the house.